Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
   
3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

• Model: LB_fit_5pH

• Model Run: HR_fitLBR_2bias_hierPcomp_5pH_infPr_uniB3_thru2023_6e+05_7kn_2025-01-14 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.8734

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

• Model development notes:
  • NA

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 8.- Residuals from logbook harvests

SWHS residuals

Figure 9.- Residuals from SWHS harvests.

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 11.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta3_yellow 5 4.633808 beta3_pH 21 2.593470 beta0_pH 27 1.963595 beta2_pH 26 1.832822 beta1_pH 30 1.694398 beta0_pelagic 4 1.673825 beta3_pelagic 1 1.585805 beta0_yellow 5 1.570240 beta1_pelagic 9 1.525257 beta2_pelagic 7 1.521971

parameter n badRhat_avg mu_beta0_pH 5 1.392373 beta0_black 2 1.315340 tau_beta0_pH 6 1.279012 beta1_yellow 5 1.229184 tau_beta0_yellow 2 1.212358 beta1_black 7 1.206588 mu_beta0_yellow 1 1.201152 beta_H 3 1.159853 beta2_yellow 2 1.152706

Table 2. Summary of unconverged parameters by area

	afognak	BSAI	CI	CSEO	eastside	EWYKT	NG	northeast	NSEI	NSEO	PWSI	PWSO	SOKO2SAP	SSEI	SSEO	WKMA
beta_H	0	0	0	0	1	0	0	0	0	0	0	0	0	0	1	1
beta0_black	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
beta0_pelagic	0	0	1	0	1	0	0	0	0	0	1	1	0	0	0	0
beta0_pH	1	1	0	1	1	1	0	1	1	1	0	0	1	1	1	1
beta0_yellow	0	0	0	1	0	0	0	0	1	1	0	1	0	0	0	1
beta1_black	1	1	0	0	1	0	1	0	0	0	1	0	1	0	0	1
beta1_pelagic	1	0	1	0	1	0	1	1	0	0	1	1	1	0	0	1
beta1_pH	0	1	1	1	1	1	1	1	1	1	1	0	1	1	1	1
beta1_yellow	1	1	0	1	0	0	0	0	1	0	0	1	0	0	0	0
beta2_pelagic	0	0	1	0	1	0	1	1	0	0	1	1	0	0	0	1
beta2_pH	1	1	1	1	1	1	0	1	1	1	0	0	1	1	1	1
beta2_yellow	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0
beta3_pelagic	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
beta3_pH	0	0	0	1	1	1	1	1	1	1	0	0	1	1	1	1
beta3_yellow	0	1	0	1	0	0	0	1	0	1	0	1	0	0	0	0
mu_beta0_pH	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
mu_beta0_yellow	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
tau_beta0_pH	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
tau_beta0_yellow	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.129	0.070	-0.262	-0.131	0.017
mu_bc_H[2]	-0.100	0.042	-0.174	-0.104	-0.009
mu_bc_H[3]	-0.431	0.074	-0.574	-0.433	-0.286
mu_bc_H[4]	-0.978	0.195	-1.382	-0.972	-0.611
mu_bc_H[5]	0.915	0.966	-0.160	0.709	3.275
mu_bc_H[6]	-2.235	0.318	-2.860	-2.234	-1.613
mu_bc_H[7]	-0.464	0.108	-0.679	-0.460	-0.260
mu_bc_H[8]	0.252	0.353	-0.332	0.219	1.069
mu_bc_H[9]	-0.315	0.137	-0.577	-0.314	-0.038
mu_bc_H[10]	-0.119	0.067	-0.247	-0.122	0.019
mu_bc_H[11]	-0.104	0.042	-0.182	-0.106	-0.019
mu_bc_H[12]	-0.246	0.104	-0.460	-0.244	-0.049
mu_bc_H[13]	-0.117	0.082	-0.266	-0.121	0.052
mu_bc_H[14]	-0.281	0.094	-0.475	-0.280	-0.105
mu_bc_H[15]	-0.345	0.054	-0.446	-0.346	-0.237
mu_bc_H[16]	-0.350	0.382	-1.003	-0.377	0.497
mu_bc_R[1]	1.341	0.144	1.075	1.341	1.626
mu_bc_R[2]	1.487	0.090	1.311	1.487	1.669
mu_bc_R[3]	1.423	0.132	1.158	1.422	1.684
mu_bc_R[4]	0.989	0.197	0.577	1.004	1.346
mu_bc_R[5]	1.157	0.451	0.272	1.163	2.050
mu_bc_R[6]	-1.544	0.433	-2.385	-1.548	-0.707
mu_bc_R[7]	0.308	0.195	-0.067	0.303	0.690
mu_bc_R[8]	0.550	0.198	0.149	0.551	0.943
mu_bc_R[9]	0.403	0.193	-0.010	0.413	0.743
mu_bc_R[10]	1.329	0.127	1.068	1.332	1.561
mu_bc_R[11]	1.134	0.078	0.983	1.133	1.291
mu_bc_R[12]	0.903	0.193	0.535	0.900	1.298
mu_bc_R[13]	1.050	0.099	0.855	1.048	1.244
mu_bc_R[14]	0.984	0.144	0.697	0.983	1.264
mu_bc_R[15]	0.881	0.097	0.689	0.883	1.062
mu_bc_R[16]	1.223	0.124	0.983	1.221	1.466
tau_pH[1]	2.821	0.293	2.269	2.811	3.429
tau_pH[2]	2.899	0.367	2.233	2.882	3.671
tau_pH[3]	2.805	0.428	2.056	2.782	3.716
tau_pH[4]	10.015	4.009	4.867	8.936	20.019
tau_pH[5]	3.951	1.972	0.148	3.988	7.989
beta0_pH[1,1]	0.528	0.227	0.062	0.539	0.965
beta0_pH[2,1]	1.345	0.218	0.918	1.351	1.770
beta0_pH[3,1]	1.367	0.235	0.890	1.375	1.803
beta0_pH[4,1]	1.654	0.276	1.041	1.664	2.153
beta0_pH[5,1]	-0.314	0.655	-1.308	-0.438	1.360
beta0_pH[6,1]	0.244	0.613	-1.014	0.378	1.147
beta0_pH[7,1]	0.328	0.549	-0.779	0.540	1.040
beta0_pH[8,1]	-0.482	0.310	-1.184	-0.444	0.030
beta0_pH[9,1]	0.070	0.869	-1.180	-0.295	1.442
beta0_pH[10,1]	0.305	0.294	-0.305	0.312	0.850
beta0_pH[11,1]	-0.004	0.494	-0.738	-0.110	1.128
beta0_pH[12,1]	0.522	0.269	-0.069	0.543	1.017
beta0_pH[13,1]	0.010	0.275	-0.525	0.004	0.567
beta0_pH[14,1]	-0.401	0.317	-1.026	-0.403	0.237
beta0_pH[15,1]	-0.243	0.647	-1.423	-0.337	1.184
beta0_pH[16,1]	1.501	1.053	-0.671	1.997	2.554
beta0_pH[1,2]	2.523	0.234	2.072	2.521	2.960
beta0_pH[2,2]	2.818	0.275	2.066	2.872	3.207
beta0_pH[3,2]	2.379	0.248	1.853	2.392	2.817
beta0_pH[4,2]	2.413	0.350	1.665	2.438	2.955
beta0_pH[5,2]	4.148	1.778	1.133	3.961	8.256
beta0_pH[6,2]	2.762	0.331	2.080	2.785	3.307
beta0_pH[7,2]	1.853	0.250	1.333	1.885	2.198
beta0_pH[8,2]	2.711	0.489	1.850	2.783	3.111
beta0_pH[9,2]	2.620	0.606	1.451	2.582	3.626
beta0_pH[10,2]	3.660	0.231	3.150	3.684	4.038
beta0_pH[11,2]	-4.927	0.258	-5.447	-4.924	-4.424
beta0_pH[12,2]	-4.957	0.480	-6.079	-4.915	-4.156
beta0_pH[13,2]	-4.709	0.399	-5.522	-4.697	-3.954
beta0_pH[14,2]	-5.751	0.493	-6.774	-5.738	-4.834
beta0_pH[15,2]	-4.165	0.303	-4.772	-4.162	-3.598
beta0_pH[16,2]	-4.922	0.379	-5.712	-4.908	-4.198
beta0_pH[1,3]	1.332	0.275	0.721	1.356	1.781
beta0_pH[2,3]	2.004	0.326	1.175	2.085	2.456
beta0_pH[3,3]	2.142	0.384	1.312	2.203	2.714
beta0_pH[4,3]	2.527	0.523	1.299	2.732	3.144
beta0_pH[5,3]	0.546	2.753	-4.428	0.775	6.004
beta0_pH[6,3]	-1.021	1.572	-2.668	-1.582	3.006
beta0_pH[7,3]	-1.897	1.253	-4.201	-1.972	0.828
beta0_pH[8,3]	0.297	0.183	-0.075	0.295	0.656
beta0_pH[9,3]	-1.047	1.541	-3.819	-0.214	0.616
beta0_pH[10,3]	0.706	0.423	-0.494	0.781	1.306
beta0_pH[11,4]	1.287	1.180	-0.773	1.596	2.773
beta0_pH[12,4]	0.299	1.590	-2.782	0.175	2.976
beta0_pH[13,4]	0.596	0.812	-0.815	0.484	2.156
beta0_pH[14,4]	0.924	1.243	-0.993	0.535	2.517
beta0_pH[15,4]	0.417	0.911	-0.762	0.166	2.459
beta0_pH[16,4]	-0.565	1.931	-4.376	-0.337	2.965
beta0_pH[11,5]	-0.238	1.581	-1.315	-0.767	4.933
beta0_pH[12,5]	-2.035	1.572	-3.123	-2.490	3.082
beta0_pH[13,5]	-0.200	0.324	-0.724	-0.191	0.419
beta0_pH[14,5]	-0.999	0.511	-2.094	-1.007	0.292
beta0_pH[15,5]	-0.904	0.721	-1.609	-1.108	1.582
beta0_pH[16,5]	-0.735	1.619	-3.607	-0.797	3.413
beta1_pH[1,1]	3.095	0.411	2.404	3.062	3.981
beta1_pH[2,1]	2.440	0.385	1.735	2.425	3.240
beta1_pH[3,1]	2.695	0.555	1.862	2.622	3.907
beta1_pH[4,1]	3.079	0.574	2.191	2.991	4.460
beta1_pH[5,1]	1.926	0.666	0.499	1.942	3.280
beta1_pH[6,1]	2.377	0.908	1.122	2.234	4.625
beta1_pH[7,1]	1.920	0.930	0.321	1.929	3.624
beta1_pH[8,1]	3.085	0.749	1.986	2.976	4.914
beta1_pH[9,1]	2.168	0.726	0.682	2.132	3.831
beta1_pH[10,1]	2.290	0.443	1.476	2.279	3.317
beta1_pH[11,1]	6.704	1.140	5.046	6.436	9.414
beta1_pH[12,1]	2.852	0.329	2.250	2.837	3.550
beta1_pH[13,1]	5.426	1.268	3.731	5.146	8.796
beta1_pH[14,1]	14.645	3.787	9.514	13.713	23.753
beta1_pH[15,1]	9.084	2.223	5.669	8.740	14.094
beta1_pH[16,1]	11.429	3.081	6.573	11.229	18.882
beta1_pH[1,2]	3.651	15.101	0.014	0.994	34.086
beta1_pH[2,2]	4.661	13.567	0.008	0.898	58.563
beta1_pH[3,2]	1.253	0.288	0.707	1.243	1.850
beta1_pH[4,2]	1.309	1.983	0.010	0.825	8.455
beta1_pH[5,2]	61.057	248.504	0.000	1.116	1169.507
beta1_pH[6,2]	1.223	1.421	0.000	1.121	3.609
beta1_pH[7,2]	3.735	25.957	0.000	0.235	7.212
beta1_pH[8,2]	0.888	2.020	0.000	0.200	7.106
beta1_pH[9,2]	1.066	0.814	0.000	1.132	2.461
beta1_pH[10,2]	21.508	41.901	0.000	2.350	162.441
beta1_pH[11,2]	6.845	0.290	6.250	6.843	7.417
beta1_pH[12,2]	6.926	0.628	5.907	6.860	8.363
beta1_pH[13,2]	7.194	0.441	6.376	7.188	8.105
beta1_pH[14,2]	7.659	0.518	6.694	7.657	8.732
beta1_pH[15,2]	6.729	0.325	6.105	6.722	7.411
beta1_pH[16,2]	7.648	0.405	6.878	7.635	8.466
beta1_pH[1,3]	1.908	0.474	1.109	1.885	2.913
beta1_pH[2,3]	0.710	1.100	0.000	0.418	4.222
beta1_pH[3,3]	0.581	0.536	0.001	0.527	1.631
beta1_pH[4,3]	0.713	0.967	0.001	0.414	3.423
beta1_pH[5,3]	6.411	8.919	1.269	3.664	27.742
beta1_pH[6,3]	5.528	10.975	1.211	3.328	25.288
beta1_pH[7,3]	2.902	1.361	0.338	2.838	5.227
beta1_pH[8,3]	2.737	0.330	2.103	2.736	3.386
beta1_pH[9,3]	3.100	1.510	1.340	2.350	5.972
beta1_pH[10,3]	2.706	0.514	1.971	2.621	4.095
beta1_pH[11,4]	2.230	1.451	0.010	2.387	5.366
beta1_pH[12,4]	2.708	1.598	0.010	2.726	5.913
beta1_pH[13,4]	1.998	0.942	0.053	2.153	3.620
beta1_pH[14,4]	5.147	8.844	0.010	2.549	40.333
beta1_pH[15,4]	1.918	0.927	0.098	2.068	3.460
beta1_pH[16,4]	8.131	8.973	2.272	4.481	34.275
beta1_pH[11,5]	13.524	11.773	1.283	9.916	38.523
beta1_pH[12,5]	40.188	104.635	3.223	12.734	394.894
beta1_pH[13,5]	14.510	17.687	2.063	7.568	65.669
beta1_pH[14,5]	24.082	30.853	0.009	4.772	86.954
beta1_pH[15,5]	6.462	4.858	1.658	4.730	19.381
beta1_pH[16,5]	12.494	16.845	0.013	2.870	57.978
beta2_pH[1,1]	0.498	0.241	0.257	0.464	0.934
beta2_pH[2,1]	0.505	0.411	0.202	0.417	1.282
beta2_pH[3,1]	0.432	0.454	0.152	0.364	1.047
beta2_pH[4,1]	0.378	0.180	0.174	0.346	0.759
beta2_pH[5,1]	1.855	4.181	-5.432	0.593	13.404
beta2_pH[6,1]	2.425	4.080	0.117	0.417	14.575
beta2_pH[7,1]	-1.432	4.303	-13.266	0.020	4.158
beta2_pH[8,1]	0.633	1.470	0.154	0.336	3.985
beta2_pH[9,1]	-3.352	5.715	-14.451	0.312	1.454
beta2_pH[10,1]	1.232	2.190	0.208	0.576	8.079
beta2_pH[11,1]	0.231	0.057	0.132	0.229	0.344
beta2_pH[12,1]	1.116	0.610	0.440	0.973	2.602
beta2_pH[13,1]	0.280	0.079	0.156	0.272	0.466
beta2_pH[14,1]	0.246	0.040	0.180	0.243	0.334
beta2_pH[15,1]	0.190	0.049	0.113	0.181	0.304
beta2_pH[16,1]	0.554	0.362	0.146	0.527	1.427
beta2_pH[1,2]	1.935	6.005	-10.617	1.803	15.109
beta2_pH[2,2]	-3.856	5.769	-16.552	-3.109	8.810
beta2_pH[3,2]	-5.354	4.282	-16.259	-4.172	-0.740
beta2_pH[4,2]	-4.876	5.237	-17.420	-3.965	4.349
beta2_pH[5,2]	-1.511	6.123	-14.160	-1.655	11.449
beta2_pH[6,2]	-4.321	5.037	-16.135	-3.674	5.560
beta2_pH[7,2]	-3.437	5.664	-15.275	-3.260	9.149
beta2_pH[8,2]	-2.565	6.151	-15.066	-2.859	12.173
beta2_pH[9,2]	-4.314	5.284	-16.078	-3.962	6.990
beta2_pH[10,2]	-5.071	5.271	-16.731	-4.604	5.949
beta2_pH[11,2]	-7.904	3.649	-17.717	-7.010	-3.644
beta2_pH[12,2]	-2.727	2.790	-10.915	-1.422	-0.522
beta2_pH[13,2]	-3.478	2.356	-9.959	-2.698	-1.316
beta2_pH[14,2]	-4.765	2.989	-12.522	-3.944	-1.560
beta2_pH[15,2]	-7.447	3.603	-16.668	-6.515	-3.482
beta2_pH[16,2]	-8.029	3.770	-17.864	-7.030	-3.635
beta2_pH[1,3]	5.016	4.192	0.349	3.792	16.467
beta2_pH[2,3]	1.994	6.325	-12.020	2.039	15.081
beta2_pH[3,3]	0.610	7.758	-15.636	1.304	17.425
beta2_pH[4,3]	1.834	6.138	-11.154	1.920	14.736
beta2_pH[5,3]	5.779	4.384	-1.442	5.226	16.033
beta2_pH[6,3]	5.986	4.782	-1.404	5.326	17.230
beta2_pH[7,3]	7.176	6.192	-2.328	5.958	21.192
beta2_pH[8,3]	8.508	4.656	1.931	7.476	20.240
beta2_pH[9,3]	5.016	4.731	0.416	4.103	16.862
beta2_pH[10,3]	5.611	4.462	0.447	4.741	16.776
beta2_pH[11,4]	2.246	6.048	-12.194	2.389	14.839
beta2_pH[12,4]	-3.673	4.114	-14.753	-2.600	0.514
beta2_pH[13,4]	0.672	4.649	-11.478	0.810	10.834
beta2_pH[14,4]	-3.893	4.438	-16.065	-2.883	1.618
beta2_pH[15,4]	0.519	4.851	-10.932	1.271	9.138
beta2_pH[16,4]	1.387	8.748	-13.705	3.798	16.394
beta2_pH[11,5]	-2.383	2.818	-10.733	-1.407	-0.290
beta2_pH[12,5]	-3.684	3.161	-11.971	-2.950	-0.483
beta2_pH[13,5]	-5.108	4.819	-18.822	-3.137	-0.878
beta2_pH[14,5]	-1.076	5.556	-13.630	-1.965	6.338
beta2_pH[15,5]	-4.927	3.785	-15.722	-3.690	-1.263
beta2_pH[16,5]	-0.713	5.533	-12.245	-1.115	12.239
beta3_pH[1,1]	35.636	1.155	33.497	35.617	37.955
beta3_pH[2,1]	34.426	1.677	31.535	34.239	38.206
beta3_pH[3,1]	36.113	2.063	32.775	35.838	41.100
beta3_pH[4,1]	36.386	1.905	33.208	36.204	40.555
beta3_pH[5,1]	29.442	4.016	20.832	28.433	39.505
beta3_pH[6,1]	40.546	3.304	32.813	41.862	45.053
beta3_pH[7,1]	34.775	9.648	19.453	38.778	45.817
beta3_pH[8,1]	38.712	1.759	35.036	38.776	42.240
beta3_pH[9,1]	28.150	5.133	18.410	30.094	35.147
beta3_pH[10,1]	32.853	1.354	30.407	32.822	35.704
beta3_pH[11,1]	36.554	2.440	33.258	36.084	42.895
beta3_pH[12,1]	30.447	0.582	29.174	30.476	31.481
beta3_pH[13,1]	38.208	2.008	35.477	37.748	43.296
beta3_pH[14,1]	41.472	1.829	38.527	41.239	45.365
beta3_pH[15,1]	41.475	2.717	36.521	41.492	45.722
beta3_pH[16,1]	44.396	1.321	40.788	44.661	45.913
beta3_pH[1,2]	37.284	7.317	19.880	40.506	44.623
beta3_pH[2,2]	29.470	6.707	18.742	28.860	43.467
beta3_pH[3,2]	41.907	0.916	40.126	41.916	43.763
beta3_pH[4,2]	35.674	8.808	19.154	40.970	45.520
beta3_pH[5,2]	31.898	8.220	18.666	31.692	45.350
beta3_pH[6,2]	35.443	4.868	21.615	35.686	45.360
beta3_pH[7,2]	30.926	7.654	18.701	31.558	45.137
beta3_pH[8,2]	30.250	7.649	18.492	29.280	44.829
beta3_pH[9,2]	40.633	7.281	20.066	44.024	45.810
beta3_pH[10,2]	29.069	5.060	19.299	29.420	41.175
beta3_pH[11,2]	43.363	0.161	43.113	43.341	43.735
beta3_pH[12,2]	43.105	0.268	42.490	43.125	43.596
beta3_pH[13,2]	43.845	0.138	43.549	43.857	44.100
beta3_pH[14,2]	43.321	0.162	43.067	43.305	43.682
beta3_pH[15,2]	43.386	0.163	43.123	43.370	43.741
beta3_pH[16,2]	43.493	0.173	43.177	43.488	43.828
beta3_pH[1,3]	40.015	0.954	37.592	40.086	41.565
beta3_pH[2,3]	31.951	7.602	18.753	32.878	45.296
beta3_pH[3,3]	33.462	7.408	19.088	33.035	44.789
beta3_pH[4,3]	29.734	7.823	18.479	28.691	45.208
beta3_pH[5,3]	28.075	6.145	18.579	27.681	43.342
beta3_pH[6,3]	31.558	4.433	20.719	32.394	42.231
beta3_pH[7,3]	25.481	3.028	20.649	24.835	33.418
beta3_pH[8,3]	41.510	0.233	41.100	41.509	41.918
beta3_pH[9,3]	32.613	1.768	29.217	33.493	34.649
beta3_pH[10,3]	35.972	0.690	33.920	36.088	36.878
beta3_pH[11,4]	36.232	6.463	28.256	36.050	45.597
beta3_pH[12,4]	41.224	3.221	29.380	42.060	45.284
beta3_pH[13,4]	33.995	4.810	29.861	31.843	44.929
beta3_pH[14,4]	37.711	5.384	28.192	40.465	44.772
beta3_pH[15,4]	35.372	6.396	29.056	31.232	45.721
beta3_pH[16,4]	33.795	6.186	28.512	29.700	43.940
beta3_pH[11,5]	37.876	2.836	31.597	38.638	41.901
beta3_pH[12,5]	38.100	2.240	32.257	38.220	42.496
beta3_pH[13,5]	40.525	0.945	38.629	40.546	43.189
beta3_pH[14,5]	37.285	3.959	29.361	38.851	43.204
beta3_pH[15,5]	40.479	0.903	38.439	40.587	42.357
beta3_pH[16,5]	36.083	5.172	28.258	37.100	45.507
beta0_pelagic[1]	2.023	0.402	0.828	2.134	2.423
beta0_pelagic[2]	1.494	0.142	1.196	1.498	1.763
beta0_pelagic[3]	0.538	0.295	-0.093	0.587	0.970
beta0_pelagic[4]	0.558	0.419	-0.384	0.522	1.193
beta0_pelagic[5]	-0.367	1.638	-3.291	-0.494	1.626
beta0_pelagic[6]	1.554	0.183	1.136	1.569	1.843
beta0_pelagic[7]	1.500	0.222	1.119	1.523	1.770
beta0_pelagic[8]	1.847	0.143	1.569	1.852	2.109
beta0_pelagic[9]	2.171	0.574	0.790	2.363	2.863
beta0_pelagic[10]	2.568	0.150	2.252	2.576	2.826
beta0_pelagic[11]	0.660	0.130	0.402	0.666	0.907
beta0_pelagic[12]	1.755	0.136	1.485	1.756	2.020
beta0_pelagic[13]	0.554	0.146	0.272	0.554	0.844
beta0_pelagic[14]	0.389	0.190	-0.003	0.403	0.741
beta0_pelagic[15]	-0.244	0.133	-0.519	-0.242	0.015
beta0_pelagic[16]	0.541	0.126	0.298	0.541	0.782
beta1_pelagic[1]	0.202	0.404	0.000	0.007	1.406
beta1_pelagic[2]	0.090	0.155	0.000	0.006	0.527
beta1_pelagic[3]	0.465	0.444	0.000	0.481	1.522
beta1_pelagic[4]	0.574	0.471	0.000	0.640	1.475
beta1_pelagic[5]	1.875	1.758	0.000	2.056	4.938
beta1_pelagic[6]	0.132	0.473	0.000	0.003	0.922
beta1_pelagic[7]	2.471	6.365	0.000	0.005	23.120
beta1_pelagic[8]	0.232	0.782	0.000	0.004	1.853
beta1_pelagic[9]	0.971	1.436	0.000	0.764	4.106
beta1_pelagic[10]	0.135	0.582	0.000	0.002	1.139
beta1_pelagic[11]	2.434	0.284	1.860	2.430	3.007
beta1_pelagic[12]	2.654	0.269	2.127	2.653	3.177
beta1_pelagic[13]	2.445	0.515	1.622	2.376	3.680
beta1_pelagic[14]	3.100	0.628	2.197	2.984	4.646
beta1_pelagic[15]	2.569	0.229	2.152	2.565	3.022
beta1_pelagic[16]	3.023	0.259	2.513	3.018	3.539
beta2_pelagic[1]	0.960	4.020	-6.978	1.029	9.353
beta2_pelagic[2]	1.076	3.856	-6.975	1.183	8.614
beta2_pelagic[3]	1.181	3.637	-6.121	0.974	9.047
beta2_pelagic[4]	1.048	3.566	-5.130	1.157	8.436
beta2_pelagic[5]	-1.711	3.675	-7.806	-2.257	7.854
beta2_pelagic[6]	-0.135	3.920	-7.756	-0.005	8.233
beta2_pelagic[7]	-0.861	4.037	-8.541	-0.936	7.807
beta2_pelagic[8]	-1.008	3.875	-8.829	-1.045	7.322
beta2_pelagic[9]	0.669	3.078	-6.329	1.521	6.340
beta2_pelagic[10]	-0.651	3.666	-7.308	-0.732	7.309
beta2_pelagic[11]	4.151	2.594	0.745	3.668	10.310
beta2_pelagic[12]	5.708	2.650	2.002	5.203	12.157
beta2_pelagic[13]	1.328	1.548	0.293	0.736	6.207
beta2_pelagic[14]	0.559	0.412	0.226	0.460	1.544
beta2_pelagic[15]	5.815	2.542	2.088	5.447	11.892
beta2_pelagic[16]	5.799	2.867	1.473	5.362	12.700
beta3_pelagic[1]	31.378	8.804	18.582	30.388	45.606
beta3_pelagic[2]	32.426	8.271	18.614	32.922	45.344
beta3_pelagic[3]	32.075	6.390	20.176	31.021	44.556
beta3_pelagic[4]	27.632	6.001	20.071	25.834	43.869
beta3_pelagic[5]	40.107	8.449	20.039	45.483	45.994
beta3_pelagic[6]	31.795	8.110	18.718	31.802	45.305
beta3_pelagic[7]	29.849	8.611	18.631	29.266	45.067
beta3_pelagic[8]	31.036	7.772	18.742	30.291	45.255
beta3_pelagic[9]	29.717	7.033	18.440	28.087	44.495
beta3_pelagic[10]	32.006	8.700	18.542	32.574	45.409
beta3_pelagic[11]	43.200	0.364	42.370	43.211	43.834
beta3_pelagic[12]	43.466	0.230	43.065	43.456	43.917
beta3_pelagic[13]	43.114	0.945	41.366	43.069	45.182
beta3_pelagic[14]	42.827	1.257	40.013	42.918	45.259
beta3_pelagic[15]	43.255	0.202	42.862	43.242	43.669
beta3_pelagic[16]	43.289	0.223	42.845	43.289	43.727
mu_beta0_pelagic[1]	1.093	0.747	-0.523	1.128	2.522
mu_beta0_pelagic[2]	1.492	0.787	-0.456	1.633	2.750
mu_beta0_pelagic[3]	0.599	0.425	-0.262	0.603	1.455
tau_beta0_pelagic[1]	1.402	1.663	0.070	0.834	5.713
tau_beta0_pelagic[2]	1.669	2.964	0.065	0.619	8.203
tau_beta0_pelagic[3]	1.908	1.419	0.210	1.588	5.514
beta0_yellow[1]	-0.546	0.191	-0.986	-0.527	-0.233
beta0_yellow[2]	0.514	0.143	0.215	0.522	0.777
beta0_yellow[3]	-0.309	0.192	-0.714	-0.298	0.018
beta0_yellow[4]	0.777	0.353	-0.384	0.856	1.172
beta0_yellow[5]	-1.216	0.409	-2.003	-1.216	-0.445
beta0_yellow[6]	0.249	0.212	-0.178	0.251	0.663
beta0_yellow[7]	0.812	0.596	-1.029	1.014	1.337
beta0_yellow[8]	0.616	0.707	-1.363	0.902	1.270
beta0_yellow[9]	-0.062	0.261	-0.543	-0.063	0.482
beta0_yellow[10]	0.243	0.149	-0.054	0.247	0.532
beta0_yellow[11]	-1.502	0.878	-2.678	-1.796	0.082
beta0_yellow[12]	-3.606	0.429	-4.516	-3.589	-2.794
beta0_yellow[13]	-3.663	0.466	-4.620	-3.661	-2.805
beta0_yellow[14]	-2.063	0.566	-3.016	-2.130	-0.448
beta0_yellow[15]	-3.010	0.459	-3.859	-2.991	-2.137
beta0_yellow[16]	-2.462	0.449	-3.419	-2.440	-1.576
beta1_yellow[1]	0.413	0.475	0.000	0.285	1.514
beta1_yellow[2]	1.012	0.234	0.587	1.001	1.512
beta1_yellow[3]	0.646	0.259	0.115	0.645	1.175
beta1_yellow[4]	1.529	1.008	0.662	1.213	4.737
beta1_yellow[5]	4.265	6.248	1.261	2.832	31.120
beta1_yellow[6]	2.285	0.342	1.624	2.282	2.969
beta1_yellow[7]	4.430	4.336	0.032	3.379	16.650
beta1_yellow[8]	2.064	1.938	0.015	1.684	7.598
beta1_yellow[9]	1.546	0.443	0.800	1.533	2.422
beta1_yellow[10]	2.640	0.607	1.740	2.579	3.682
beta1_yellow[11]	2.292	0.819	0.805	2.222	4.613
beta1_yellow[12]	2.397	0.435	1.591	2.373	3.290
beta1_yellow[13]	2.849	0.458	2.018	2.835	3.793
beta1_yellow[14]	2.155	0.504	1.002	2.200	3.065
beta1_yellow[15]	2.313	0.460	1.433	2.297	3.184
beta1_yellow[16]	2.275	0.453	1.339	2.261	3.210
beta2_yellow[1]	-2.791	2.874	-9.417	-2.366	2.211
beta2_yellow[2]	-3.139	2.288	-9.087	-2.600	-0.354
beta2_yellow[3]	-3.029	2.524	-9.362	-2.346	-0.182
beta2_yellow[4]	-2.513	2.521	-8.930	-1.751	-0.071
beta2_yellow[5]	-4.146	2.926	-11.369	-3.525	-0.415
beta2_yellow[6]	3.667	2.236	0.974	3.096	9.172
beta2_yellow[7]	-3.199	3.998	-10.731	-3.490	5.157
beta2_yellow[8]	-1.634	4.159	-10.001	-1.461	7.085
beta2_yellow[9]	3.886	2.563	0.297	3.473	9.755
beta2_yellow[10]	-4.799	2.799	-11.342	-4.274	-0.904
beta2_yellow[11]	-2.843	2.022	-7.389	-2.565	-0.048
beta2_yellow[12]	-3.632	2.003	-8.805	-3.231	-1.114
beta2_yellow[13]	-3.473	1.761	-8.352	-3.080	-1.364
beta2_yellow[14]	-3.680	2.161	-9.338	-3.215	-0.676
beta2_yellow[15]	-3.159	1.770	-7.798	-2.757	-0.887
beta2_yellow[16]	-3.806	2.082	-9.270	-3.376	-1.218
beta3_yellow[1]	29.763	8.255	18.432	28.815	45.316
beta3_yellow[2]	29.269	1.308	27.410	28.970	32.587
beta3_yellow[3]	33.363	2.880	28.418	33.125	40.458
beta3_yellow[4]	28.869	3.592	20.386	27.966	35.744
beta3_yellow[5]	33.085	2.182	26.614	33.399	36.033
beta3_yellow[6]	39.653	0.513	38.761	39.616	40.838
beta3_yellow[7]	22.271	5.062	18.459	20.283	39.314
beta3_yellow[8]	26.768	6.151	18.441	26.171	43.837
beta3_yellow[9]	37.825	1.921	36.289	37.625	42.777
beta3_yellow[10]	29.307	0.788	28.112	29.403	30.018
beta3_yellow[11]	40.174	7.496	28.271	45.193	45.974
beta3_yellow[12]	43.418	0.466	42.548	43.366	44.517
beta3_yellow[13]	44.855	0.399	43.959	44.922	45.510
beta3_yellow[14]	43.932	2.350	34.359	44.232	45.821
beta3_yellow[15]	45.414	0.444	44.407	45.501	45.979
beta3_yellow[16]	44.619	0.638	43.500	44.588	45.848
mu_beta0_yellow[1]	0.089	0.547	-1.045	0.097	1.196
mu_beta0_yellow[2]	0.105	0.477	-0.879	0.119	1.015
mu_beta0_yellow[3]	-2.334	0.695	-3.421	-2.444	-0.596
tau_beta0_yellow[1]	1.867	2.134	0.092	1.197	7.105
tau_beta0_yellow[2]	1.564	2.112	0.162	1.054	5.609
tau_beta0_yellow[3]	1.427	2.205	0.076	0.786	6.586
beta0_black[1]	-0.081	0.151	-0.378	-0.085	0.211
beta0_black[2]	1.768	0.546	0.731	1.860	2.128
beta0_black[3]	1.133	0.559	-1.202	1.257	1.531
beta0_black[4]	2.032	0.273	1.368	2.051	2.484
beta0_black[5]	1.589	2.020	-2.985	1.641	5.634
beta0_black[6]	1.563	1.931	-2.815	1.625	5.499
beta0_black[7]	1.524	1.947	-2.806	1.611	5.424
beta0_black[8]	1.260	0.223	0.815	1.262	1.685
beta0_black[9]	2.413	0.255	1.912	2.418	2.902
beta0_black[10]	1.460	0.128	1.215	1.462	1.709
beta0_black[11]	3.350	0.331	2.380	3.398	3.720
beta0_black[12]	4.477	0.187	4.109	4.478	4.846
beta0_black[13]	-0.107	0.222	-0.548	-0.099	0.300
beta0_black[14]	2.038	0.606	0.504	2.206	2.765
beta0_black[15]	1.081	0.304	0.247	1.142	1.509
beta0_black[16]	3.962	0.574	2.309	4.144	4.532
beta2_black[1]	3.628	2.326	0.835	3.064	9.667
beta2_black[2]	-0.227	4.099	-8.556	-0.483	8.092
beta2_black[3]	0.559	4.239	-8.296	0.617	9.148
beta2_black[4]	-2.470	2.971	-9.444	-1.960	3.242
beta2_black[5]	-0.115	4.311	-8.733	-0.057	8.410
beta2_black[6]	-0.199	4.246	-8.376	-0.279	8.225
beta2_black[7]	-0.117	4.307	-8.541	-0.072	8.326
beta2_black[8]	-0.264	4.314	-8.904	-0.265	8.334
beta2_black[9]	-0.141	4.343	-8.508	-0.220	8.851
beta2_black[10]	-0.293	4.213	-8.669	-0.369	7.953
beta2_black[11]	-2.202	2.475	-7.986	-1.824	2.648
beta2_black[12]	-2.926	1.796	-7.593	-2.478	-0.678
beta2_black[13]	-2.439	1.936	-7.737	-1.824	-0.512
beta2_black[14]	-1.794	2.033	-7.364	-0.985	-0.100
beta2_black[15]	-2.193	2.179	-7.603	-1.732	0.394
beta2_black[16]	-1.040	2.988	-7.603	-0.741	5.147
beta3_black[1]	41.771	0.858	40.082	41.883	43.033
beta3_black[2]	31.206	8.286	18.396	31.864	45.200
beta3_black[3]	30.393	8.325	18.386	30.000	45.205
beta3_black[4]	33.331	3.741	22.532	33.215	41.456
beta3_black[5]	32.055	8.056	18.604	32.125	45.340
beta3_black[6]	31.988	8.223	18.639	31.820	45.442
beta3_black[7]	32.131	8.118	18.789	32.351	45.227
beta3_black[8]	32.040	8.094	18.840	31.996	45.231
beta3_black[9]	32.113	8.034	18.683	32.194	45.092
beta3_black[10]	31.739	8.070	18.780	31.307	45.386
beta3_black[11]	35.043	4.757	28.326	34.116	45.026
beta3_black[12]	32.838	0.725	30.934	32.947	33.884
beta3_black[13]	39.330	0.679	37.863	39.403	40.436
beta3_black[14]	38.977	3.056	32.468	39.142	45.370
beta3_black[15]	37.394	5.193	28.596	37.519	45.466
beta3_black[16]	35.739	5.636	28.156	35.057	45.652
beta4_black[1]	-0.257	0.189	-0.633	-0.252	0.103
beta4_black[2]	0.247	0.176	-0.107	0.249	0.590
beta4_black[3]	-0.939	0.184	-1.299	-0.939	-0.586
beta4_black[4]	0.537	0.214	0.125	0.536	0.971
beta4_black[5]	0.293	2.441	-4.374	0.197	5.235
beta4_black[6]	0.202	2.550	-4.365	0.138	4.730
beta4_black[7]	0.225	2.627	-4.346	0.192	4.928
beta4_black[8]	-0.688	0.363	-1.371	-0.684	0.010
beta4_black[9]	1.495	1.064	-0.100	1.335	3.917
beta4_black[10]	0.024	0.180	-0.328	0.022	0.373
beta4_black[11]	-0.695	0.205	-1.102	-0.690	-0.303
beta4_black[12]	0.307	0.323	-0.295	0.296	0.967
beta4_black[13]	-1.190	0.213	-1.615	-1.190	-0.789
beta4_black[14]	-0.122	0.230	-0.560	-0.128	0.351
beta4_black[15]	-0.883	0.202	-1.277	-0.876	-0.489
beta4_black[16]	-0.593	0.224	-1.037	-0.597	-0.150
mu_beta0_black[1]	1.136	0.873	-0.855	1.180	2.787
mu_beta0_black[2]	1.565	0.901	-0.561	1.626	3.297
mu_beta0_black[3]	2.229	0.968	0.203	2.268	4.091
tau_beta0_black[1]	0.784	0.775	0.065	0.546	2.861
tau_beta0_black[2]	1.934	3.695	0.060	0.839	9.713
tau_beta0_black[3]	0.254	0.171	0.049	0.214	0.695
beta0_dsr[11]	-3.038	0.269	-3.565	-3.036	-2.531
beta0_dsr[12]	4.481	0.260	3.980	4.481	5.002
beta0_dsr[13]	-1.581	0.278	-2.121	-1.580	-1.033
beta0_dsr[14]	-4.075	0.461	-4.987	-4.071	-3.222
beta0_dsr[15]	-2.393	0.266	-2.934	-2.385	-1.890
beta0_dsr[16]	-3.042	0.342	-3.732	-3.029	-2.397
beta1_dsr[11]	4.909	0.283	4.366	4.914	5.465
beta1_dsr[12]	5.843	3.035	2.489	5.100	13.906
beta1_dsr[13]	3.030	0.287	2.470	3.029	3.589
beta1_dsr[14]	6.707	0.495	5.780	6.707	7.674
beta1_dsr[15]	3.573	0.267	3.052	3.572	4.106
beta1_dsr[16]	5.829	0.358	5.125	5.821	6.540
beta2_dsr[11]	-8.744	2.408	-14.313	-8.363	-4.916
beta2_dsr[12]	-7.601	2.700	-13.551	-7.411	-2.738
beta2_dsr[13]	-7.441	2.768	-12.681	-7.505	-2.252
beta2_dsr[14]	-7.088	2.500	-12.491	-6.914	-2.732
beta2_dsr[15]	-8.055	2.395	-13.443	-7.788	-4.132
beta2_dsr[16]	-8.271	2.415	-13.820	-7.967	-4.533
beta3_dsr[11]	43.484	0.152	43.211	43.479	43.773
beta3_dsr[12]	34.034	0.648	32.339	34.170	34.812
beta3_dsr[13]	43.231	0.238	42.914	43.160	43.817
beta3_dsr[14]	43.241	0.135	43.073	43.206	43.614
beta3_dsr[15]	43.473	0.189	43.143	43.465	43.823
beta3_dsr[16]	43.436	0.160	43.174	43.426	43.765
beta4_dsr[11]	0.671	0.207	0.255	0.669	1.077
beta4_dsr[12]	0.321	0.462	-0.578	0.316	1.248
beta4_dsr[13]	-0.084	0.210	-0.495	-0.084	0.329
beta4_dsr[14]	0.205	0.248	-0.286	0.204	0.709
beta4_dsr[15]	0.993	0.212	0.579	0.990	1.414
beta4_dsr[16]	0.173	0.227	-0.272	0.173	0.633
beta0_slope[11]	-2.003	0.157	-2.303	-2.005	-1.701
beta0_slope[12]	-4.679	0.262	-5.212	-4.677	-4.173
beta0_slope[13]	-1.458	0.243	-2.092	-1.423	-1.097
beta0_slope[14]	-2.646	0.215	-3.058	-2.653	-2.215
beta0_slope[15]	-1.716	0.154	-2.042	-1.712	-1.416
beta0_slope[16]	-2.756	0.166	-3.088	-2.753	-2.435
beta1_slope[11]	4.396	0.287	3.832	4.392	4.960
beta1_slope[12]	4.818	0.542	3.763	4.815	5.881
beta1_slope[13]	2.802	0.689	2.007	2.633	4.882
beta1_slope[14]	6.102	0.905	4.641	5.990	8.298
beta1_slope[15]	2.039	0.282	1.471	2.044	2.574
beta1_slope[16]	5.290	0.395	4.546	5.289	6.094
beta2_slope[11]	7.623	2.450	3.866	7.253	13.152
beta2_slope[12]	5.732	2.590	1.556	5.456	11.660
beta2_slope[13]	4.358	3.057	0.262	4.010	11.264
beta2_slope[14]	2.272	1.885	0.698	1.404	6.875
beta2_slope[15]	5.605	3.101	2.057	4.539	13.440
beta2_slope[16]	7.379	2.845	2.928	6.881	13.098
beta3_slope[11]	43.493	0.149	43.216	43.489	43.775
beta3_slope[12]	43.374	0.242	42.993	43.342	43.873
beta3_slope[13]	43.614	0.585	42.476	43.624	45.123
beta3_slope[14]	44.685	0.438	43.785	44.726	45.427
beta3_slope[15]	43.591	0.259	43.110	43.591	44.101
beta3_slope[16]	43.470	0.171	43.169	43.465	43.808
beta4_slope[11]	-0.463	0.204	-0.872	-0.462	-0.059
beta4_slope[12]	-1.228	0.672	-2.764	-1.143	-0.175
beta4_slope[13]	0.177	0.208	-0.231	0.177	0.578
beta4_slope[14]	-0.122	0.249	-0.602	-0.122	0.371
beta4_slope[15]	-0.185	0.201	-0.573	-0.190	0.212
beta4_slope[16]	-0.139	0.222	-0.572	-0.138	0.307
sigma_H[1]	0.196	0.051	0.102	0.193	0.304
sigma_H[2]	0.171	0.030	0.117	0.169	0.236
sigma_H[3]	0.198	0.042	0.126	0.196	0.292
sigma_H[4]	0.421	0.080	0.293	0.413	0.606
sigma_H[5]	0.982	0.218	0.599	0.967	1.452
sigma_H[6]	0.378	0.204	0.022	0.371	0.807
sigma_H[7]	0.300	0.061	0.210	0.291	0.446
sigma_H[8]	0.427	0.092	0.289	0.413	0.652
sigma_H[9]	0.504	0.121	0.318	0.486	0.785
sigma_H[10]	0.219	0.042	0.144	0.215	0.314
sigma_H[11]	0.278	0.047	0.199	0.273	0.385
sigma_H[12]	0.444	0.165	0.210	0.426	0.776
sigma_H[13]	0.215	0.039	0.147	0.212	0.298
sigma_H[14]	0.509	0.093	0.342	0.503	0.707
sigma_H[15]	0.249	0.041	0.182	0.245	0.339
sigma_H[16]	0.232	0.046	0.159	0.226	0.338
lambda_H[1]	3.088	3.946	0.149	1.705	14.046
lambda_H[2]	8.359	7.809	0.855	5.985	28.918
lambda_H[3]	5.901	8.538	0.278	3.026	29.349
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	3.991	9.800	0.025	0.897	30.999
lambda_H[6]	8.220	16.780	0.009	0.686	58.859
lambda_H[7]	0.014	0.010	0.002	0.011	0.040
lambda_H[8]	8.201	11.139	0.002	4.500	38.853
lambda_H[9]	0.016	0.012	0.003	0.014	0.045
lambda_H[10]	0.318	0.788	0.031	0.197	1.195
lambda_H[11]	0.261	0.398	0.011	0.127	1.245
lambda_H[12]	4.941	6.366	0.203	2.926	21.981
lambda_H[13]	3.205	2.880	0.247	2.375	11.513
lambda_H[14]	3.582	4.397	0.252	2.193	15.900
lambda_H[15]	0.028	0.096	0.003	0.017	0.108
lambda_H[16]	1.762	2.220	0.094	1.047	7.754
mu_lambda_H[1]	4.357	1.889	1.267	4.174	8.371
mu_lambda_H[2]	3.837	1.996	0.555	3.707	7.972
mu_lambda_H[3]	3.605	1.831	0.841	3.386	7.813
sigma_lambda_H[1]	8.612	4.308	2.086	7.948	18.202
sigma_lambda_H[2]	8.376	4.759	0.882	7.812	18.495
sigma_lambda_H[3]	6.329	3.904	1.088	5.574	16.299
beta_H[1,1]	6.862	1.120	4.162	7.064	8.542
beta_H[2,1]	9.878	0.492	8.820	9.899	10.739
beta_H[3,1]	8.016	0.770	6.195	8.103	9.314
beta_H[4,1]	9.094	7.948	-7.005	9.236	23.742
beta_H[5,1]	0.100	2.479	-4.997	0.274	4.373
beta_H[6,1]	3.084	4.012	-6.924	4.576	7.663
beta_H[7,1]	0.755	5.742	-11.492	1.166	11.179
beta_H[8,1]	2.356	7.686	-2.416	1.277	32.157
beta_H[9,1]	13.293	5.735	1.794	13.262	24.787
beta_H[10,1]	7.102	1.746	3.388	7.216	10.468
beta_H[11,1]	5.331	3.290	-2.190	6.029	9.928
beta_H[12,1]	2.558	1.071	0.793	2.496	4.766
beta_H[13,1]	9.039	0.869	7.094	9.097	10.571
beta_H[14,1]	2.192	1.002	0.193	2.170	4.239
beta_H[15,1]	-5.990	3.930	-13.126	-6.297	2.259
beta_H[16,1]	2.985	1.932	-0.501	2.908	7.371
beta_H[1,2]	7.906	0.244	7.403	7.912	8.370
beta_H[2,2]	10.028	0.131	9.771	10.031	10.282
beta_H[3,2]	8.956	0.199	8.571	8.949	9.360
beta_H[4,2]	3.596	1.510	0.843	3.519	6.766
beta_H[5,2]	1.949	0.965	0.038	1.994	3.765
beta_H[6,2]	5.801	1.087	3.296	5.981	7.446
beta_H[7,2]	2.542	1.106	0.502	2.438	4.977
beta_H[8,2]	2.760	1.883	-4.570	3.128	4.249
beta_H[9,2]	3.323	1.108	1.238	3.279	5.640
beta_H[10,2]	8.178	0.349	7.437	8.190	8.821
beta_H[11,2]	9.703	0.593	8.811	9.600	11.047
beta_H[12,2]	3.934	0.370	3.291	3.922	4.709
beta_H[13,2]	9.096	0.256	8.631	9.087	9.639
beta_H[14,2]	4.010	0.342	3.354	4.006	4.689
beta_H[15,2]	11.357	0.702	9.892	11.395	12.646
beta_H[16,2]	4.718	0.773	3.159	4.726	6.192
beta_H[1,3]	8.480	0.238	8.054	8.466	8.972
beta_H[2,3]	10.079	0.115	9.853	10.079	10.301
beta_H[3,3]	9.612	0.165	9.293	9.609	9.941
beta_H[4,3]	-2.531	0.892	-4.357	-2.513	-0.788
beta_H[5,3]	3.889	0.628	2.618	3.889	5.080
beta_H[6,3]	8.196	1.221	6.491	7.828	10.799
beta_H[7,3]	-2.611	0.738	-4.099	-2.595	-1.161
beta_H[8,3]	5.360	0.842	4.629	5.193	8.646
beta_H[9,3]	-2.570	0.798	-4.131	-2.571	-0.974
beta_H[10,3]	8.753	0.278	8.213	8.752	9.288
beta_H[11,3]	8.547	0.273	7.950	8.566	9.024
beta_H[12,3]	5.252	0.320	4.514	5.292	5.769
beta_H[13,3]	8.813	0.187	8.430	8.817	9.170
beta_H[14,3]	5.685	0.271	5.127	5.703	6.154
beta_H[15,3]	10.362	0.326	9.747	10.354	11.021
beta_H[16,3]	6.733	0.496	5.603	6.795	7.536
beta_H[1,4]	8.275	0.175	7.909	8.285	8.596
beta_H[2,4]	10.137	0.117	9.885	10.144	10.349
beta_H[3,4]	10.111	0.166	9.746	10.128	10.397
beta_H[4,4]	11.776	0.459	10.830	11.790	12.654
beta_H[5,4]	5.585	0.810	4.272	5.486	7.407
beta_H[6,4]	7.159	0.898	5.059	7.409	8.345
beta_H[7,4]	8.221	0.343	7.560	8.218	8.880
beta_H[8,4]	6.649	0.352	5.452	6.693	7.110
beta_H[9,4]	7.163	0.459	6.295	7.148	8.093
beta_H[10,4]	7.759	0.243	7.319	7.748	8.256
beta_H[11,4]	9.296	0.206	8.917	9.286	9.709
beta_H[12,4]	7.127	0.215	6.721	7.117	7.586
beta_H[13,4]	8.998	0.145	8.709	8.998	9.284
beta_H[14,4]	7.661	0.212	7.252	7.661	8.090
beta_H[15,4]	9.446	0.241	8.962	9.444	9.919
beta_H[16,4]	9.152	0.206	8.789	9.140	9.592
beta_H[1,5]	8.975	0.144	8.681	8.978	9.256
beta_H[2,5]	10.780	0.093	10.605	10.776	10.978
beta_H[3,5]	10.925	0.176	10.616	10.912	11.292
beta_H[4,5]	8.386	0.476	7.503	8.368	9.398
beta_H[5,5]	5.329	0.631	3.869	5.398	6.411
beta_H[6,5]	8.793	0.589	7.929	8.658	10.241
beta_H[7,5]	6.790	0.334	6.126	6.785	7.437
beta_H[8,5]	8.229	0.290	7.854	8.192	9.076
beta_H[9,5]	8.224	0.465	7.311	8.239	9.127
beta_H[10,5]	10.086	0.236	9.633	10.083	10.553
beta_H[11,5]	11.533	0.232	11.046	11.539	11.963
beta_H[12,5]	8.475	0.202	8.078	8.474	8.890
beta_H[13,5]	10.012	0.131	9.761	10.012	10.268
beta_H[14,5]	9.185	0.230	8.756	9.175	9.678
beta_H[15,5]	11.178	0.249	10.699	11.184	11.669
beta_H[16,5]	9.957	0.161	9.633	9.960	10.277
beta_H[1,6]	10.184	0.188	9.860	10.165	10.631
beta_H[2,6]	11.512	0.107	11.305	11.512	11.727
beta_H[3,6]	10.801	0.166	10.444	10.812	11.090
beta_H[4,6]	12.870	0.820	11.177	12.904	14.439
beta_H[5,6]	5.919	0.616	4.808	5.898	7.181
beta_H[6,6]	8.816	0.626	7.144	8.920	9.699
beta_H[7,6]	9.828	0.551	8.791	9.820	10.919
beta_H[8,6]	9.473	0.403	8.390	9.526	9.957
beta_H[9,6]	8.476	0.763	6.985	8.473	10.018
beta_H[10,6]	9.516	0.321	8.824	9.540	10.072
beta_H[11,6]	10.803	0.347	10.079	10.819	11.429
beta_H[12,6]	9.377	0.258	8.883	9.368	9.919
beta_H[13,6]	11.062	0.160	10.765	11.055	11.405
beta_H[14,6]	9.869	0.286	9.298	9.873	10.409
beta_H[15,6]	10.852	0.438	9.985	10.843	11.696
beta_H[16,6]	10.571	0.206	10.112	10.588	10.941
beta_H[1,7]	10.876	0.887	8.771	10.974	12.355
beta_H[2,7]	12.213	0.432	11.313	12.212	13.063
beta_H[3,7]	10.543	0.675	9.097	10.602	11.662
beta_H[4,7]	2.513	4.136	-5.385	2.448	11.021
beta_H[5,7]	6.588	1.995	3.099	6.415	11.345
beta_H[6,7]	9.486	2.329	4.673	9.515	14.894
beta_H[7,7]	10.627	2.770	5.155	10.658	15.857
beta_H[8,7]	11.153	1.646	9.394	10.916	15.467
beta_H[9,7]	4.335	3.945	-3.789	4.365	11.923
beta_H[10,7]	9.841	1.448	7.238	9.743	12.958
beta_H[11,7]	11.016	1.696	7.888	10.888	14.696
beta_H[12,7]	9.999	0.964	7.901	10.079	11.580
beta_H[13,7]	11.652	0.746	9.859	11.747	12.839
beta_H[14,7]	10.484	0.937	8.473	10.559	12.194
beta_H[15,7]	12.227	2.263	7.806	12.237	16.727
beta_H[16,7]	11.921	1.035	10.234	11.758	14.487
beta0_H[1]	8.997	14.399	-17.640	8.836	37.031
beta0_H[2]	10.581	6.239	-2.372	10.554	23.485
beta0_H[3]	9.749	9.942	-11.357	9.978	29.850
beta0_H[4]	5.456	185.380	-361.337	2.257	399.662
beta0_H[5]	4.411	28.375	-47.394	4.132	62.453
beta0_H[6]	6.882	49.764	-94.045	7.807	103.716
beta0_H[7]	7.920	130.230	-253.837	6.150	287.805
beta0_H[8]	6.423	57.488	-25.156	6.392	38.183
beta0_H[9]	7.849	118.933	-236.497	6.625	249.971
beta0_H[10]	8.593	33.216	-60.098	8.856	76.972
beta0_H[11]	8.895	48.885	-92.101	8.676	113.873
beta0_H[12]	6.956	11.685	-16.341	7.009	28.581
beta0_H[13]	9.389	11.512	-11.557	9.573	30.613
beta0_H[14]	6.448	10.931	-16.475	6.759	27.985
beta0_H[15]	9.817	104.590	-198.380	9.620	215.435
beta0_H[16]	8.149	17.289	-28.964	8.274	41.021